Maxwell's Equations:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla \cdot D= \rho [/tex]

[tex]\nabla \cdot B=0[/tex]

[tex]\nabla \times E=- \partial B/ \partial t[/tex]

[tex]\nabla \times H=J+ \partial D/ \partial t[/tex]

Together with the continuity eq:

[tex]\nabla \cdot J=- \partial \rho / \partial t[/tex]

There are 9 scalar equations and 16 scalar unknowns (B, E, D, H, J, [tex]\rho [/tex])

If we are supplied with the relations that relate B to H and E to D (e.g. a linear media relation):

D=f(E)

H=g(B)

we have 6 more scalar equations and therefore 15 equations in total. We are still one equation short of solving the Maxwell Eq, if we are supplied with appropriate B.C. and Initial Conditions, and we do not constrain the current density J and charge density [tex]\rho[/tex]. In that case, how do we solve the Maxwell Equations?

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# Maxwell's Equations: are they complete?

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